The on-loan Liverpool striker netted his fourth goal in the last five appearances for the Irons in Saturday's 1-1 draw at Southampton but Allardyce revealed committing to such one marquee signing could just prove too costly.
"The hardest thing is the overall package, the overall negotiation which needs to go on to make sure it can be sustainable in terms of what we can do," said Allardyce. "I will still point towards financial restrictions being implemented next season - they could blow the whole deal in one go."
Premier League clubs last week voted through new regulations which will limit how much of the new television income can be spent on wage bills and there could even be points penalties for severe breaches of the guidelines.
Allardyce added: "So in one fell swoop the financial restrictions mean Andy Carroll can't sign for us from Liverpool because it's too expensive, even if he wanted to.
"Somebody will have a bigger budget than us somewhere, but I tell you that is what's going to happen, I might not be able to afford Andy Carroll, full stop, even if I wanted him, even if the chairmen wanted him, even if we all wanted him, which we do, it will not be allowed to happen."
Allardyce believes it will take some time before the true impact of the new regulations, which have been brought in to try to level the playing field in the top flight, can be felt.
"I suppose across the board when you first introduce something new the fair/unfair scenario has to get sorted out somewhere along the line to find out how you have to tweak it to make it better," he said.
"But if we want Andy Carroll, or any player, and you look at the whole thing, you are going to have to move very quickly now because your budget is going to say that (figure) and you are not allowed to go over that apparently, and because you are not allowed to go over that.
"You have to say (to the player) 'sorry and off you go', so then it is very difficult to improve your side from last season."